Can I add emojis to touch bar globally?

No. Currently there is no native way to do this and I doubt any third parties have managed to.

Each app has to build its own specific functionality for the touch bar. Depending on what view you’re on (i.e. composing vs reading email) on which app (mail vs safari) there is typically an option to "customize touch bar" in the menu on the top left of your screen that will be specific to that view.

Customize allows you to pick certain things you can add to your touch bar. Emojis are available in Mail and Safari (in addition to messages).

"Customize control strip" (in System Preferences) lets you edit the 4 slots that are always present on the right of the touch bar in addition to the view of the whole touch bar when you click the expansion arrow. These interact with the computer directly, not the app that you are using.

Update: Chrome now supports touch bar! Still no emoji button on the Mac or chrome strip...hopefully it will arrive soon.

Mac Emoji Keyboard Shortcut: ctrl + cmd + space

Just tried this app and it works: https://github.com/gabriellorin/touch-bar-emojis

Shows frequently used ones only, though.